Department of Mathematics and Applied ... - up.ac.za

Department of Mathematics and Applied

Mathematics

Departement Wiskunde en Toegepaste Wiskunde

GRADES 8 AND 9 GRADE 8 EN 9

26 July – 1 Aug 2021 26 July – 1 Aug 2021

TIME: 2 HOURS TYD: 2 URE

©2012 OUTEURSREG VOORBEHOU, UNIVERSITEIT VAN PRETORIA

©2012 COPYRIGHT RESERVED, UNIVERSITY OF PRETORIA

Question 1 Vraag 1

Recall that 1.234 = 1.234343434 . . . Which ofthe following is closest to 1?

Onthou dat 1.234 = 1.234343434 . . . Wattervan die volgende getalle is die naaste aan 1?

(A) 0.95 (B) 1.05 (C) 1.040 (D) 0.95 (E) 0.960

Question 2 Vraag 2

Which one of the following figures cannotbe drawn without lifting your pen off thepage and without drawing along the same linetwice?

Watter een van die volgende figure kan niegeteken word sonder om jou pen op te lig nieen ook nie twee keer oor dieselfde lyn te treknie?

Question 3 Vraag 3

What is the remainder when 1234 × 5678 isdivided by 5?

Wat is die res as 1234 × 5678 deur 5 gedeelword?

(A) 0 (B) 1 (C) 2 (D) 3 (E) 4

Question 4 Vraag 4

What is the value of (4 − 14) ÷ (2 − 1

2)? Wat is die waarde van (4 − 14) ÷ (2 − 1

2)?

(A) 278 (B) 3

2 (C) 2 (D) 52 (E) 3

Question 5 Vraag 5

Aneesu do not like multiples of 3. She counts1, 2, 4, 5, 7, 8, 10, 11, . . . avoiding multiples of3. Note that the 5th number on the list is 7.What is the 55th number on her list?

Aneesu hou nie van veelvoude van 3nie. Sy tel 1, 2, 4, 5, 7, 8, 10, 11, . . . en vermyveelvoude van 3. Let op dat die 5de getal opdie lys is 7. Wat is die 55ste getal op haarlys?

(A) 79 (B) 82 (C) 83 (D) 85 (E) None of these/Geen van hierdie

Question 6 Vraag 6

2021−2020+2019−2018+. . .+5−4+3−2+1equals

2021−2020+2019−2018+. . .+5−4+3−2+1is gelyk aan


1

Question 7 Vraag 7

What fraction of the figure is shaded? Watter breuk van die figure is ingekleur?

(A)13

16(B)

13

32(C)

1

2(D)

9

16(E)

5

8

Question 8 Vraag 8

The value of 2448816 is Die waarde van 2448816 is

(A) 216 (B) 252 (C) 268 (D) 284 (E) 292

Question 9 Vraag 9

On the highway to Pretoria, the speed limit is120 km/h. The fine for exceeding this speedis R105 for each km/h. If the fine received isR9450, at what speed was the motorist driv-ing?

Op die snelweg na Pretoria, is die spoedgrens120 km/h. Die boete as jy die spoed oorskryis R105 vir elke km/h. As die boete R9450 is,teen watter spoed het die bestuurder gery?

(A) 180km/h (B) 190km/h (C) 200km/h (D) 210km/h (E) 220km/h

Question 10 Vraag 10

Find the value of x in the diagram below. Bepaal die waarde van x in die diagramhieronder.

(A) 162 (B) 108 (C) 138 (D) 158 (E) 152

2


If7

u− 5

4=

5

6, then u equals As

7

u− 5

4=

5

6, dan is u gelyk aan

(A) 3.16 (B) 3.26 (C) 3.36 (D) 3.46 (E) 3.56


Let a, b, and c be real numbers such thatc < a < 0 < b. Which of the following is apositive real number? (That is a real numberbigger than zero.)

Laat a, b en c reele getalle wees sodat c <a < 0 < b. Watter een van die volgende is’n positiewe reele getal? (Dit is ’n reele getalgroter as nul.)

(A) (c− a) b (B) a3bc2 (C) (b− c)a (D) a2bc (E) ab2c3


The figure below consists out of 5 squares.If AB = 30 meters, what is the area of theentire figure in meter squares?

Die figuur hieronder bestaan uit 5 vierkante.As AB = 30 meter, wat is die oppervlaktevan die hele figuur in vierkante meter?

(A) 300 (B) 450 (C) 400 (D) 900 (E) 500


In the sequence a, b, c, d, 18, 32, 59, 110 eachterm after the first four terms is the sum ofthe previous four terms. The first term of thesequence is

In die ry a, b, c, d, 18, 32, 59, 110 is elke termna die vierde term die som van die vorige vierterme. Die eerste term van die ry is

(A) 3 (B) 9 (C) 8 (D) 1 (E) 4

3


Define the function R(n) that reverses thedigits of n and S(n) that adds all the digits ofn. For example, R(435) = 534 and S(435) =4 + 3 + 5 = 12. Suppose n is a four-digitnumber such that R(n) + S(n) = 2021. Ifx is the biggest solution and y the smallestsolution, determine x− y.

Laat R(n) die getal wees wat die syfers van nomdraai en S(n) die som van die syfers vann. Byvoorbeeld, R(435) = 534 en S(435) =4+3+5 = 12. Laat n ’n vier-syfer getal weessodat R(n) +S(n) = 2021. As x die grootsteoplossing is en y die kleinste oplossing, bepaalx− y.



The time 2021 minutes after 20 : 21 on adigital 24-hour clock is

Die tyd 2021 minute na 20 : 21 op ’n elek-troniese 24-uur horlosie is

(A) 03 : 02 (B) 04 : 02 (C) 05 : 02 (D) 06 : 02 (E) None of these/Geen van hierdie


Each of the factors of 100 is to be placed in a3 by 3 grid, one per cell, in such a way thatthe products of the three numbers in eachrow, column and diagonal are all equal. Thepositions of the numbers 1, 2, 50 are shown inthe diagram. What is the value of U + P?

Al die faktore van 100 moet in ’n 3 by 3blokkie geplaas word, een per blokkie, sodatdie produkte van die drie getalle in elke ry,kolom en hoeklyn gelyk is aan mekaar. Dieposisies van die getalle 1, 2, 50 word in die di-agram getoon. Wat is die waarde van U +P?


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Each of four dwarfs is either normal or mu-tant. A normal dwarf has four eyes and al-ways lies. A mutant dwarf has either threeor five eyes and always tells the truth. Whenasked how many eyes they have among them,their respective responses are 13, 14, 15 and16. The total number of eyes among thesefour dwarfs is

Elkeen van vier dwergies is normaal of mu-tant. ’n Normale dwerg het vier oe en jokaltyd. ’n Mutante dwerg het drie of vyf oeen praat altyd die waarheid. Op die vraaghoeveel oe hulle het, antwoord hulle: 13, 14,15 en 16. Die totale aantal oe onder hierdievier dwergies is

(A) 13 (B) 14 (C) 15 (D) 16 (E) Cannot be determined/Kan nie bepaal word nie


Bart Simpson wrote all the 6-digit integerscontaining all the digits 1, 2, 3, 4, 5, 6 exactlyonce on a board. How many of these numbersare divisible by 8?

Bart Simpson skryf al die 6-syfer getalle watal die syfers 1, 2, 3, 4, 5, 6 presies een keer be-vat op ’n bord. Hoeveel van die getalle isdeelbaar deur 8?



Thabo, Tumi and Thandi are students in thesame mathematics class that wrote a test.The average mark of all students in the classexcept Thabo is 63.1. The average mark ofall the students in the class except Thaboand Tumi is 62. The average mark of all stu-dents in the class except Thabo, Tumi andThandi is 60.625. If you know, Thabo, Tumiand Thandi got the same mark for the mathstest, how many students are in the class?

Thabo, Tumi en Thandi is in dieseldewiskunde klas wat ’n toets geskryf het. Diegemiddelde punt vir die toets vir die hele klasbehalwe, Thabo is 63.1. Die gemiddelde puntvir die toets vir die hele klas behalwe, Thaboen Tumi is 62. Die gemiddelde punt vir dietoets vir die hele klas behalwe, Thabo, Tumien Thandi is 60.625. As jy weet dat Thabo,Tumi en Thandi dieselfde punt gekry het virdie wiskunde toets, hoeveel studente is in dieklas?

(A) 10 (B) 11 (C) 12 (D) 13 (E) Not enough information/Nie genoeg inligting

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Department of Mathematics and Applied ... - up.ac.za